Abstarct: Entangled states are the baxses of non-locality for a composite system in quantum mechanics. By exploiting entangled states, we can perform tasks in quantum mechanics that are difficult or impossible classically. Non-orthogonal states can not reliably be distinguished in quantum mechanics. Moreover the operation of cloning the unknown quantum state is impossible. But this is not the story in the classical mechanics. So if a quantum mechanical system is made up of several orthogonal un-entangled states, the quantum system would behave entirely classically and would not exhibit any non-locality [1,2]. In other words, it ought to be possible to discover the orthogonal un-entangled states and also to be possible to clone these states baxsed on local operation and classical communications. In this dissertation, for a composite quantum system made up of two physical systems with two observers, Alice and Bob, we obtain an ensemble composed of 16 orthogonal un-entangled states in a sixteen-dimensional Hilbert space, so that these states are not orthogonal as seen by Alice or Bob alone. By mathematical and quantum mechanical calculations for these states, we can quantitative measures be computed, such as mutual information obtainable, entropies due to state preparation and measurement, and quantity "advice of measurement" which each show non-locality behavior of system during measurement protocol on states. Then by comparing the outcomes of this ensemble with outcomes of 9 states ensemble (un-entangled states in 3×3 Hilbert space) [24], we conclude that an ensemble of states in a greater Hilbert space exhibit non-local behavior with better results with more probability of success than a shorter Hilbert space. We suggest usage of a greater Hilbert space for Alice and Bob yields to optimal results.